+0

This isn't a question, I just think the solution is interesting

+5
585
2
+981

Emily is twice as old as Charlotte. Four years ago, the product of their ages was 30. Use a quadratic equation to find Charlotte's present age.

First I said E (Emily) = 2C (Charlotte)

Then . . .

(E-4)*(C-4)=30

EC-4E-4C+16=30

EC-4E-4C=14

EC-4E-4C-14=0

Next I substituted in [E=2C]

(2C*C)-(2C*4)-4C-14=0

2C^2-8C-4C-14=0

2C^2-12C-14=0

Then I factorised . . .

2*(C^2-6C-7)=0

2*(C-7)*(C+1)=0

So Charlotte's present age must be 7.

To check it . . .

E=2*7=14

(E-4)*(C-4)=30

(14-4)*(7-4)=30

10*3=30

I thought this might interest at least one person.

zacismyname  May 3, 2015

#2
+981
+5

Nice

I didn't think of doing it like that. The more direct route for sure.

zacismyname  May 3, 2015
#1
+92744
+5

Very nice, zacismyname   !!!   ....you're correct.....this is a good one  !!!

We could also do it with one varable from the start :

Let Charlotte's age be x  and Emily's age be 2x

So we have

(2x - 4)(x - 4) = 30

2x^2 - 12x + 16 = 30

2x^2 - 12x - 14 = 0

x^2 - 6x - 7  = 0

(x - 7) (x + 1) = 0      so x = 7 or  x = -1   .....reject  - 1  .....

So.....x = 7  = Charlotte's age     and 2(7)  = 14 = Emily's age

Just as you found  !!!!

CPhill  May 3, 2015
#2
+981
+5